A355083 E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(exp(x) - 1).

1, 2, 10, 86, 1106, 19562, 451014, 13051586, 460907034, 19434738686, 961628831658, 55046140338642, 3602414472002206, 266842000568643866, 22180625837341816898, 2053584526860808500094, 210393497508897167616290, 23715128208081620773251530

Offset: 0

Author

Seiichi Manyama, Jun 19 2022

Keywords

• nonn

Crossrefs

Cf. A213357, A355092.

Cf. A355100.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, j*stirling(i, j, 2)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(log(1+x)) = 1 + 2*x*A(x).

a(0) = 1; a(n) = 2 * Sum_{k=1..n} k * Stirling2(n,k)* a(k-1).